彩色数字全息的非插值波面重建算法研究

彩色数字全息及多波长照明的数字全息检测研究中，避免插值误差的可变放大率波面重建是一个重要的研究内容.由于Fresnel衍射积分可以表示成Fourier变换及卷积两种形式，对应地存在两种波面重建算法：其一,将重建距离分为两段的衍射“接力”算法；其二,用球面波为重建波的卷积算法.文中对这两种算法进行理论分析及实验研究，讨论让重建计算满足取样定理的条件.结果表明，卷积算法较容易满足取样定理，能够获得较好的重建物光场. 关键词： 彩色数字全息 波面重建 衍射计算

Algorithm of the non-interpolation wave-front reconstruction of the color digital holography

In the research of the color digital holography and digital holography measurement with multi-wavelength illumination, how to avoid the interpolation error in the wave-front reconstruction with variable magnification is an important subject to be studied. Since the Fresnel diffraction integral can be expressed as Fourier transformation as well as convolution form, there are two reconstruction approaches, one is the relay algorithm which divides the reconstruction distance into two parts, the other is the convolution algorithm which uses the spherical wave as reconstruction wave. In this paper, the two algorithms are theoretically analyzed and experimentally studied, and the condition satisfying the sampling theorem for the reconstruction calculation is discussed. The results show that the convolution approach satisfies the sampling theorem more readily, while higher quality reconstructed object wave field can be obtained with the convolution approach.